Article pubs.acs.org/IC
5d Metal(IV) Imide Complexes. The Impact (or Lack Thereof) of d‑Orbital Occupation on Methane Activation and Functionalization Catherine A. Moulder† and Thomas R. Cundari*,†,‡ †
Department of Chemistry and ‡Center for Advanced Scientific Computing and Modeling (CASCaM), University of North Texas, 1155 Union Circle, #305070, Denton, Texas 76203-5017, United States ABSTRACT: This research evaluates 5d metal imide complexes, (OH)2MNMe (M = W, Re, or Os), and their reactions with methane to form dimethylamine. Each is calculated to follow a consistent reaction pathway regardless of the metal’s d-orbital occupation, whereby the methane C−H bond undergoes oxidative addition (OA) to the metal and then the methyl migrates from the metal to the nitrogen to form an amide. Finally, hydrogen migrates to the nitrogen before dissociating to form amine products. While homolytic M−imide, M−amide M−H, and M−CH3 bond dissociation free energies (BDFEs) were analyzed, the BDFEs of neither hexavalent nor tetravalent metal moieties reflect the oxidative addition kinetics. Instead, a strain theory approach, supported by electron density analysis for the OA transition state, is found to be explanatory. Notably, the rate-determining step, the hydrogen migration transition state, has a consistent jump in free energy versus the preceding intermediate, (OH)2MIV(H) N(CH3)Me, for all metals evaluated. Thus, the height of the RDS is largely reflective of the stability of the MIV−amide intermediate, suggesting a strategy for viable catalysis.
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INTRODUCTION Hydrocarbons store an abundance of energy in their C−H bonds, which is generally harvested via combustion. Methane is the major component of natural gas, and there are environmental and economic concerns about its release into the atmosphere. A catalytic method for selectively functionalizing a methane C−H bond and yielding a product that retains a significant portion of the energy from its C−H bonds that also yields a more easily transportable liquid would be of immense economic and environmental benefit.1 The main challenge lies in the C−H bonds of light alkanes, which are notoriously inert.2 Reagents powerful enough to activate these aliphatic C−H bonds are also easily capable of further reacting with the products of the initial reactions, thus limiting selectivity.3 Carbon−nitrogen bonds are important for applications such as medicine, pharmacology, and polymer synthesis.4,5 Currently, many C−N bond formations are catalyzed with palladium, an expensive reagent, via coupling chemistry, which requires multiple synthetic steps. Ideally, C−N bonds could be synthesized via direct activation and functionalization of a C− H bond by a nitrene (NR) functionality.6,7 This work is a computational study of middle series, thirdrow (5d) transition metal imide (NR2−) complexes, models of reagents known to activate C−H and H−H bonds.8 Utilizing mechanisms proposed in the literature, the current study focuses on specific transition states that may allow strong, inert aliphatic bonds to be activated with a focus on the role of the metal−nitrogen active site. To date, most studies of earthabundant metal catalysis have focused on 3d metals.9,10 Strong © XXXX American Chemical Society
5d metal−imide bonds are expected to make nitrene transfer to a methane C−H bond endergonic. However, a better understanding is sought through a theory of how different heavy metals (with different d counts) change the free energy landscape of prototypical methane functionalization catalytic steps. Using the proposal of Wolczanski and Schaller that the imide needs to have a strongly electrophilic metal and a metal-based acceptor orbital, three-coordinate metal(IV) imide models were generated.11 In 1991, Eppley et al. reported a three-coordinate, W(IV) imide, W(OSitBu3)2(NtBu), which is known to activate H2 (bond energy of ∼104 kcal/mol).8 A computational study of methane activation by a W(OH)2(NH) model was reported, utilizing Hartree−Fock and Møller−Plesset methods.12 An experimental and computational study of intramolecular C−H activation by a d2 WIV imide complex triggered by Lewis base coordination was recently published.13 The current model utilizes simple OH ligands, rather than bulky alkoxide and siloxide ligands used experimentally,12,13 to focus upon the impact of changing the electronic structure of the MN active site through amelioration of steric considerations. Through the use of density functional theory, potential reaction mechanisms for methane activation and functionalization were compared and low-energy pathways discovered. On the basis of literature precedent,2,3,6−13 three primary transition states/ reaction pathways were tested: oxidative addition, [2+2] Received: September 8, 2016
A
DOI: 10.1021/acs.inorgchem.6b02157 Inorg. Chem. XXXX, XXX, XXX−XXX
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Inorganic Chemistry addition, and hydrogen atom abstraction (Figure 1). Of particular interest is the fact that the mechanisms entail
Scheme 1. Qualitative Free Energy Diagram of Each Reaction Pathway Modeled, Oxidative Addition (blue), [2+2] Addition (brown), and Hydrogen Atom Abstraction (purple)a
Figure 1. Transition states investigated for methane C−H activation by a model metal imide complex, for which M = W, Re, or Os. Note that throughout this work the methyl group (CH3) from the methane substrate is distinguished from the imide methyl substituent, which is denoted as Me.
activation directed at the metal, metal−ligand, and ligand portion, respectively, of the complex active site. The [2+2] pathway11,12 entails the concurrent (or nearly so) addition of the carbon and hydrogen of a methane C−H bond across the metal−nitrogen multiple bond. Oxidative addition involves both the carbon and hydrogen of the methane substrate interacting simultaneously with the metal atom to form metal− methyl and metal−hydrogen bonds, respectively.8,12,13 In hydrogen atom abstraction (HAA),14 the imide nitrogen abstracts the hydrogen from methane, yielding a methyl radical, which may then rebound to the metal or imide nitrogen. Of course, in HAA and related pathways (like proton-coupled electron transfer),15 the metal interacts indirectly with the three-center N···H···C active site, and its redox state is formally modulated.
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a
Note that the oxidative addition, [2+2], and HAA (lowest energy) pathways are unified (red pathway) after the initial mechanistic steps to form the M(OH)2(N(H)Me)(CH3) intermediate.
COMPUTATIONAL METHODS
Calculations were obtained using the Gaussian 09 software16 for molecules in the gas phase at standard temperature and pressure. The BP86 functional17 for the heavy atoms is used in conjunction with the CEP-31G basis set.18 The basis sets are augmented with a d polarization function. This level of theory was chosen on the basis of previous research,19 which calibrated the level of theory versus higher-level ab initio techniques. All species are modeled as neutrals with all appropriate spin multiplicities tested. Free energies are reported in kilocalories per mole. Minima are defined by having zero imaginary vibrational frequencies, whereas transition states have one imaginary vibrational frequency.
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RESULTS AND DISCUSSION Trends as a Function of Metal. While a d0 metal imide is expected to activate C−H bonds by a [2+2] pathway,11,12 the current models are formally d2 (WIV), d3 (ReIV), and d4 (OsIV). Calculations indicate that instead of direct formation of the [2+2] addition product, MIV(OH)2(N(H)Me)(CH3), the preferred pathway for methane activation by all three imide complexes involves C−H oxidative addition (Scheme 1). Interestingly, the lowest-energy pathway from imide reactant to amine product for all three metals occurs via the same four steps: oxidative addition, methyl migration, hydrogen migration, and finally product dissociation (Figure 2). Note that while the methyl transfer and hydrogen transfer are labeled as “migrations”, they can also be described as reductive eliminations given the changes in the formal oxidation state of the metal; however, as the methyl and hydrogen move to a far greater degree than the nitrogen-based ligands in the calculated imaginary modes, the term “migration” is used to denote this distinction. Inverting the migration sequence to hydrogen and then methyl entails an ∼13 kcal/mol free energy penalty due to the higher barrier for the latter of these two
Figure 2. Reaction pathways explored with the lowest-energy spin state and relative free energy (kilocalories per mole) listed for each complex studied. Each metal is color-coded with the spin states for each intermediate listed on the left and the relative Gibbs free energy below such that tungsten is colored red, rhenium blue, and osmium green. The optimal energy reaction pathway is on the right and highlighted with the large arrows.
steps, i.e., the conversion of the H3C−M IV −N(H)Me functionality to the ligated product, MII←N(H)(CH3)(Me). B
DOI: 10.1021/acs.inorgchem.6b02157 Inorg. Chem. XXXX, XXX, XXX−XXX
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change in thermodynamic preference for Os (ΔG = −9.7 kcal/ mol). This may be interpreted as arising from a weakening of the strength of the metal−imide π-bond from left to right in this 5d series, and thus a potentially controlling factor in the preferred pathway for initial methane C−H activation. However, further analysis of metal−ligand bond energies is needed (Figure 2). The metal−nitrogen π-bond order is reduced in the reaction that produces the second intermediate (Figure 5), (OH)2-
It is interesting to note that unlike d0 imides, these middle series complexes are apparently not basic enough at the imide nitrogen (nor presumably acidic enough at the metal) to deprotonate the weak Brønsted acid methane (pKa ∼ 50). Moreover, the open-shell ReIV imido (doublet ground state) has very little spin density on the imide nitrogen (−0.09 e−), which implies this nitrogen has little radical character, while the other imide reagents have none as ground state singlets. No evidence of open-shell singlets was found for W or Os(OH)2(NMe). Unlike earlier d0 metal imide complexes, [2+2] addition of methane across the MN linkage is not thermodynamically favored11,12 (Figure 2) [ΔG2+2 = +18.4 (W), +14.0 (Re), and +1.2 (Os) kcal/mol], with very high computed kinetic barriers of >55 kcal/mol (Figure 2). Thus, it appears that as long as the metal has two d electrons, oxidative addition is the preferred pathway. Figures 3 and 4 show
Figure 5. Density functional theory-optimized transition state for CH3 migration to convert OsVI imide to OsIV amide: bond lengths in angstroms and bond angles in degrees.
(CH3)MVI(H)NMe → (OH)2MIV(H)N(CH3)Me; the metal amide maintains some degree of π-bonding as seen by the ∼360° sum of bond angles about the amide nitrogen. The metal formal oxidation state is also returned to the +4 state from the +6 state of the square pyramidal intermediate, making this methyl migration step a reductive process at the metal. Interestingly, methyl migration is mildly exergonic for osmium (ΔGMM1 = −6.1 kcal/mol) but endergonic [+23.0 and +12.7 kcal/mol for the earlier metals, tungsten and rhenium, respectively (Figure 2)]. Methyl migration is an important reaction in alkane functionalization, and previous research indicated a similar trend for C−O bond formation reactions among a series of 3d metal complexes.20 This work suggests that similar trends identified for C−O formation mediated by 3d metals also apply to C−N bond formation and 5d metals. After the initial methyl migration from the OA product to make (OH)2MIV(H)N(CH3)Me, the hydride ligand must migrate across the metal−amide bond to form the ligated dimethylamine product (Figure 6), (OH)2MIV(H)N(CH3)Me → (OH)2MII ← NH(CH3)Me. Any metal−nitrogen
Figure 3. Density functional theory-optimized transition state for oxidative addition of CH3−H to Os(OH)2(NMe): bond lengths in angstroms and bond angles in degrees.
Figure 4. Density functional theory-optimized product of methane C− H oxidative addition to Os(OH)2(NMe): bond lengths in angstroms and bond angles in degrees.
geometries for a typical oxidative addition transition state (OA⧧) and intermediate, respectively, for M = Os. The preference for oxidative addition is intriguing in that one might expect that the stronger N−H bond formed in the [2+2] pathway would provide a thermodynamic advantage vis-à-vis the weaker M−H bond formed upon oxidative addition. Figure 2 shows that MIV(OH)2(CH3)(N(H)Me), the [2+2] intermediate, is higher in free energy than MVI(OH)2(CH3)(H)( NMe), the OA intermediate, for the earlier two 5d metals, W (ΔG = 14.2 kcal/mol) and Re (ΔG = 6.4 kcal/mol), with a
Figure 6. Density functional theory-optimized transition state amide to ammine interconversion via hydrogen migration: bond lengths in angstroms and bond angles in degrees. C
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based orbitals are a nonbonding dz2 orbital (HOMO−1, not plotted) and a dyz orbital (HOMO), the latter of which is antibonding with respect to the π orbitals but has no Nimide character. It is the LUMO that corresponds to the M−Nimide πantibonding orbital (Figure 7). In combination with the data
multiple bond is lost in the reaction that produces the dative intermediate. As with the other elementary reactions in the reaction sequence, there is a congruity among these metals despite their differing d-orbital counts in that this H migration is the rate-determining step (RDS) for all three complexes. The relative (to separated reactions) free energies for each RDS are 75.8, 69.1, and 56.1 kcal/mol for W, Re, and Os, respectively (Figure 2, right-hand pathway). The free energies for the RDS are on average ∼13 kcal/mol less expensive than the alternative pathway of migrating the hydrogen first and then the methyl group, with ΔGrel values of 90.1, 81.6, and 67.7 kcal/mol for W, Re, and Os, respectively (Figure 2, central pathway). Overall, the final product relative free energies are 70.5 kcal/ mol for W, 63.1 kcal/mol for Re, and 50.7 kcal/mol for Os. While the reactions are highly endergonic, and the RDS barriers are too high for a practical catalyst system (as expected given the strength of typical M5d−imide multiple bonds), it is intriguing to see how rapidly the barriers fall from left to right in the transition series (Figure 2). Trends in Metal−Ligand Bond Free Energies. Metal− Imide and Metal−Amide Bond Strengths. Although the different 5d metals are computed to activate and functionalize methane by the same pathway, there are nevertheless interesting thermodynamic and kinetic trends as a function of metal (and thus d-orbital occupation) for the overall functionalization as well as the individual mechanistic steps. Computed homolytic bond dissociation free energies were analyzed for possible insight into these trends. Table 1 shows
Figure 7. Osmium−imido reactant HOMO dyz on the left and LUMO dxz on the right. The IsoValue is 0.045.
listed in Table 1, this leads to the hypothesis that weakening of the metal−nitrogen π-bond in this series of 5d metals is not due to the increasing occupation of orbitals with M−Nimide πantibonding character, but rather some other factor such as reduced overlap between metal and nitrogen orbitals as one traverses to the right and the metal’s effective nuclear charge increases. Metal−Carbon and Metal−Hydrogen Bond Strengths. It is postulated that the thermodynamics (and presumably kinetics via the Hammond postulate) of methane C−H oxidative addition reflects the strengths of the two bonds formed, MVI−H and MVI−CH3. The BDFEs of the MVI−H and M VI −CH 3 bonds were initially derived from the M VI intermediate generated by oxidative addition, viz., square pyramidal (H)(CH3)(OH)2MN(CH3) (see Figure 4 for the example of M = Os). From these data, the bond dissociation free energies for the M−H bond are 49 kcal/mol for W, 51 kcal/mol for Re, and 56 kcal/mol for Os (Table 2), a
Table 1. Calculated Thermodynamic Bond Dissociation Free Energies for Metal−Nitrogen Bonds in Kilocalories per Mole metal
MN BDFE
M−N BDFE
MN → M−N ΔBDFE
W Re Os
115 107 95
64 59 59
51 49 36
Table 2. Calculated Bond Dissociation Free Energies for MVI−Hydrogen and MVI−Methyl Bonds in Kilocalories per Mole and Sums of These in Relation to the BDFE of Methane (95 kcal/mol)
the bond dissociation free energies for the metal−imide and metal−amide bonds calculated via homolysis of the MIV(OH)2(NMe) reactant and MIV(OH)2(N(H)Me)(CH3) intermediate, respectively. It is reasonable to assume that the relative values as a function of metal will be accurate even if the absolute values of the BDFEs may be less so. From the BDFEs listed in Table 1, the MN (metal−imide) bond strength decreases from 115 kcal/mol (d2 WIV) to 107 kcal/mol (d3 ReIV) and even more markedly to 95 kcal/mol (d4 OsIV). The metal−imide BDFEs are calculated from the free energy change of (OH)2MIVNMe → (OH)2MII + 3NMe. The metal−amide BDFEs are calculated from the free energy difference between (CH3)(OH)2MIVN(H)Me and methylaminyl radical (2NHMe•) with M(OH)2CH3. The metal− amide bond (predominantly a σ-bond) also weakens from W to Os (64 > 59 ∼ 59 kcal/mol), but much less dramatically (the range is one-quarter of that computed for MN BDFEs) than the metal−imide bonds strengths (Table 1). It is possible to approximate the metal−nitrogen π-bond strength as the difference in metal−imide and metal−amide BDFEs (right column of Table 1). As the number of d electrons on the metal increases, there is a decrease in the strength of the π-bond while there is little modulation of the strength of the σbond, particularly upon going from Re to Os. This is interesting in that for d4-OsIV(OH)2(NMe), the doubly occupied metal-
metal
MVI−H BDFE
MVI−CH3 BDFE
sum vs methane BDFE
W Re Os
49 51 56
37 35 34
−9 −9 −5
surprisingly small spread. The BDFEs for the M−CH3 moiety are 37 kcal/mol for W, 35 kcal/mol for Re, and 34 kcal/mol for Os, which is even less variance than that calculated for the M− H bonds. Summing up the bond energies of the methyl−metal and hydrogen−metal bonds gives an estimate of the total energy released by the formation of the new metal−ligand bonds. Using the same theoretical protocols, the C−H bonds in methane have a calculated BDFE of 95 kcal/mol. Subtracting out the free energy costs of breaking the methane C−H BDFE from the sum of the free energies released by the formation of the methyl−metal and hydrogen−metal bonds gives a sense of the relevant thermodynamic differences in the oxidative addition reaction. The data in Table 2 (right column) show very little variation as a function of metal. As such, the MVI−H and MVI−CH3 bond strengths do not rationalize the decrease D
DOI: 10.1021/acs.inorgchem.6b02157 Inorg. Chem. XXXX, XXX, XXX−XXX
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sum to 338° for tungsten, 352° for rhenium, and 355° for osmium. This trend in the sum of the angles at the metal indicates that for the OA transition state, the metal pyramidalizes, but apart from the W complex, this geometric perturbation is minimal. However, the imide complexes are apparently strongly planar, and the computed strain energies for the imide complex to reach its TS geometry are 18.0, 22.3, and 16.7 kcal/mol for W, Re, and Os, respectively (Table 5),
in oxidative addition barriers as one traverses from the W imide to the Re imide to the Os imide. As noted previously, BDFEs for H−MVI and H3C−MVI bonds, the hexavalent moieties, also do not reflect the oxidative addition thermodynamics or kinetics. Thus, the H−MIV and H3C−MIV BDFEs were investigated as being responsible for the free energy differences as a function of metal in the OA pathways. These bond strengths were calculated from the free energy changes of the following reactions: MIV(H)(OH)2(N(CH3)Me) → H• + [MIII(OH)2(N(CH3)Me)]• for BDFE(MIV−H) and MIV(CH3)(OH)2(NHMe) → Me• + [MIII(OH)2(NHMe)]• for BDFE(MIV−CH3). The data in Table 3
Table 5. Calculated Strain Energies (electronic energies, kilocalories per mole) for Methane and MIV(OH)2(NMe) Fragments in the Oxidative Addition Transition Statea
Table 3. Calculated Bond Dissociation Free Energies for MIV−Hydrogen and MIV−Methyl Bonds in Kilocalories per Mole and Sums of These in Relation to the BDFE of Methane (95 kcal/mol) metal
MIV−H BDFE
MIV−CH3 BDFE
sum vs methane BDFE
W Re Os
64 60 64
49 43 45
18 8 14
a
metal
ΔE⧧
CH4 strain
imide strain
∑strain
ΔEint
W Re Os
22.1 17.6 12.6
11.2 24.3 30.4
18.0 22.3 16.7
29.2 46.6 47.1
−7.1 −29.0 −34.5
ΔE⧧ is the activation electronic energy; ΔEint = ΔE⧧ − ∑Estrain.
which are comparable to, but with much less variation than, Estrain(CH4). Summing up the methane and M(OH)2(NMe) strain energies and using the equation ΔE⧧ = ∑Estrain + ΔEint, the interaction energies are listed in Table 5. The strain theory implies that the greater interaction energy (ΔEint = ΔE⧧ − ∑ΔEstrain) between the CH3···H and M(OH)2(NMe) fragments in the oxidative addition TSs from left to right among the three 5d metals studied which counterbalances the greater energy needed for the reactants to distort to reach the oxidative addition TS (Table 5). In support of this assertion, plotting the electron density for each oxidative addition transition state shows clear evidence of stronger interaction between the methane C−H bond and the metal in the following order: W < Re < Os (Figure 8). Concomitant with this, there is the obvious depletion of electron density of the methane C−H bond being activated.
illustrate that the BDFEs of M−CH3 and M−H bonds in the tetravalent state are, on average, ∼10−12 kcal/mol stronger for the metals in the tetravalent state than for those in the hexavalent state. However, as with the sum of the hexavalent metal−methyl and metal−hydride bond strengths, the tetravalent metal−methyl and metal−hydride bonds do not reflect the computed trends in oxidative addition thermodynamics or kinetics. Structural and Bonding Analysis of Oxidative Addition and Hydrogen Migration Transition States. The geometries and bonding of the key methane C−H oxidative addition and hydrogen migration transition states were analyzed. As the metal moves to the right, the C−H bonds of the methane substrate become increasingly longer, by ∼0.15 Å (Table 4). At the same time, the M−C and M−H bonds Table 4. Bond Lengths (angstroms) at the Active Site for the Oxidative Addition Transition State metal
C−H
M−C
M−H
W Re Os
1.265 1.369 1.413
2.537 2.355 2.314
1.851 1.749 1.691
become markedly shorter, by ∼0.2 Å for both bonds. The metal−ligand shortening may be primarily attributed to the trend of decreased covalent radii moving to the right (W, 1.62 Å; Re, 1.51 Å; Os, 1.44 Å).21 Hence, the longer C−H distances in OA⧧ are reflective of earlier transition states for W versus Re and in turn Os (Table 4). Using a strain theory analysis like that espoused by Bickelhaupt,22,23 one would predict that longer C−H bonds in OA⧧ reflect greater energetic input needed for the CH3−H substrate to reach the transition state. Indeed, this is supported by calculating the strain energy of the methane fragment in the OA transition states relative to ground state methane (electronic energies were utilized): 11.2 (W), 24.3 (Re), and 30.4 (Os) kcal/mol. The imide reactant starts in a trigonal planar geometry, which means that the ligand−metal−ligand bond angles sum to 360°. The transition state has angles that
Figure 8. Plot of the total electron density for the oxidative addition transition states of W, Re, and Os. The IsoValue is 0.10.
This section closes with the note that for the hydride migration TS, HM⧧, which represents the highest point on the computed reaction coordinates, the transition states are a near constant 50 kcal/mol in free energy above the (OH)2MIV(H)− N(CH3)Me intermediates (Figure 2). As with the oxidative addition TSs, the M−H distances in the migration transition state more or less track with the covalent radii of the metals (Table 6). Additionally, there is only modest variation (ca. ±0.04 Å) among the H−N and M−N distances in HM⧧ (Table 6). This hydrogen migration, which largely describes the conversion of the metal−amide σ-bond into a dative bond, leads to the interesting conclusion that it is the investment of this M−N σ-bond of the amide rather than the M−N π-bond of E
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but much less dramatically (Table 1). Analysis of the frontier orbitals indicates that the weakening of the M−N π-bond upon moving to the right in this series is not due to the increasing level of occupation of orbitals with the M−Nimide π-antibonding character, but perhaps some other factor such as a reduced overlap between the metal and nitrogen orbitals. The BDFEs of MIV−CH3 and MIV−H bonds are, on average, ∼10−12 kcal/mol stronger than the corresponding hexavalent BDFEs (Table 3), while a similar congruency in relative bond strengths as a function of metal is maintained. However, neither hexavalent nor tetravalent BDFEs reflect the calculated trends in oxidative addition barriers. A different source was thus investigated to explain the trends in oxidative addition. Moving from tungsten to rhenium to osmium, the free energy necessary to effect oxidative addition of the methane C−H bond decreases. Analyzing changes in C−H, M−C, and M−H bond lengths in the oxidative addition TS versus the relevant bonds in the ground states (Table 4) leads to the conclusion that they are reflective of earlier transition states for W compared to Re, and for Re compared to Os. A strain theory approach was evaluated.22,23 By calculation of the stain energies of both the methane and the imide constituents of the OA transition states, it was found that while the CH4 strain increased significantly upon moving rightward in the 5d series, the energetic variation of imide complex strain was less significant. Increasing energy of interaction upon moving from W to Re to Os was thus identified as a key factor in the observed trends in methane C−H oxidative addition barriers (Table 5). A plot of the electron density for each oxidative transition state (Figure 8) provided evidence of stronger interaction between the methane C−H bond and each metal in the series W < Re < Os, concomitant with a decrease in the electron density between the H3C and H fragments. The metal−nitrogen π-bond is reduced with the initial migration of the methyl from the metal to nitrogen (imide → amide) (Figure 5). Interestingly, the computed trends in methyl migration barriers computed here are similar to those reported for methyl migration in C−O bond forming reactions among a series for 3d metal−methyl complexes.20 The ratedetermining step is the migration of hydrogen (amide → amine) from the metal to nitrogen after the initial methyl migration (Scheme 2). The relative free energies of the ratedetermining steps are 75.8, 69.1, and 56.1 kcal/mol for W, Re, and Os, respectively. Interestingly, the rate-determining step, the hydride migration TS, is consistently 50 kcal/mol higher in free energy than the preceding intermediate, (OH)2MIV(H)− N(CH3)Me. Given that the height of the rate-determining step is reflective of the stability of the MIV−amide intermediate, this suggests that the identification of ligand sets to stabilize this intermediate may be important for catalytic methane functionalization.
Table 6. Bond Lengths (angstroms) for Each Bond of the Active Site of the Optimized Rate-Determining Step (OH)2(H)MIVN(CH3)Me → (OH)2MII ← NH(CH3)Me metal
M−H
H−N
M−N
W Re Os
1.929 1.876 1.734
1.260 1.225 1.317
2.085 2.038 2.078
the imide that is more important in determining the utility of complete activation/functionalization catalytic cycles for metal−imide complexes. This hypothesis echoes similar deductions from research about H2 and C−H activation by RuII amides24 and C−H activation/functionalization by Ni imides.25 It is concluded, therefore, that the height of this ratedetermining step is largely reflective of ground state rather than transition state effects, i.e., the stability of the MIV−amide intermediate.
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SUMMARY, CONCLUSION, AND PROSPECTUS This research models 5d metal imide complexes, (OH)2MIV NMe, and their reactions with methane to form dimethylamine. Prior research indicates that a d0 metal imide will activate the C−H bond of methane by a [2+2] pathway,11,12 whereas the complexes modeled here are formally d2−4. The different metals studied here follow a consistent reaction pathway (Scheme 2), Scheme 2. Free Energy Diagram of the Lowest-Energy Pathway, Contrasting the 5d Metalsa
a
As in Figure 2, W is colored red, Re blue, and Os green for the relative Gibbs free energy values listed by each stationary point.
regardless of d-orbital occupation, whereby the methane C−H bond oxidatively adds to the metal center, then the methyl migrates from the metal to the nitrogen to form an amide, then the hydrogen migrates to the nitrogen, and finally dissociates to form amine products. While HAA and [2+2] addition were explored (Scheme 1 and Figure 2), the lack of radical character on the imide N in the ground state of (HO)2MIV(NMe) disfavors the former while the latter pathway is disfavored by the strength of the metal−imide π-bond. Homolytic M−imide, M−amide M−H, and M−CH3 BDFEs were analyzed to gain insight into the individual mechanistic steps. The calculated metal−imide π-bond strengths (assumed to be the difference in metal−imide and metal−amide BDFEs) supported the hypothesis about the critical role of the metal− imide bond strength in the selection of the most favored pathway; however, it is notable that the metal−amide bond weakens upon moving from W to Os (64 > 59 ∼ 59 kcal/mol),
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Catherine A. Moulder: 0000-0002-0943-6498 Notes
The authors declare no competing financial interest. F
DOI: 10.1021/acs.inorgchem.6b02157 Inorg. Chem. XXXX, XXX, XXX−XXX
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MP2 and density functional (BP86) study. Chem. Phys. 1996, 206, 57− 61. (18) Stevens, W. J.; Basch, H.; Krauss, M. Compact effective potentials and efficient shared-exponent basis sets for the first- and second-row atoms. J. Chem. Phys. 1984, 81, 6026−6033. (19) Khani, S. K.; Cundari, T. R. A comprarision of the SimmonsSmith reaction with carbenoids to netrenoids and oxenoids. Comput. Theor. Chem. 2015, 1056, 61−73. (20) Garrett, E. C., III; Figg, T. M.; Cundari, T. R. Impact of dOrbital Occupation on Metal−Carbon Bond Functionalization. Inorg. Chem. 2014, 53, 7789−7798. (21) Winter, M. WebElements. https://www.webelements.com/ (accessed April 2016). (22) van Zeist, W.; Visser, R.; Bickelhaupt, F. M. The Steric Nature of the Bite Angle. Chem. - Eur. J. 2009, 15, 6112−6115. (23) van Zeist, W. J.; Bickelhaupt, F. M. The activation strain model of chemical reactivity. Org. Biomol. Chem. 2010, 8, 3118−3127. (24) Conner, D.; Jayaprakash, K. N.; Cundari, T. R.; Gunnoe, T. B. Synthesis and reactivity of a coordinatively unsaturated ruthenium (II) parent amido complex: Studies of XH activation (X= H or C). Organometallics 2004, 23, 2724−2733. (25) Cundari, T. R.; Morello, G. R. A Computational Study of MetalMediated Decomposition of Nitrene Transfer Reagents. J. Org. Chem. 2009, 74, 5711−5714.
ACKNOWLEDGMENTS The authors acknowledge support of this research through National Science Foundation Grant CHE-1464943. C.A.M. acknowledges the University of North Texas Honors College for an Undergraduate Research Fellowship.
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DOI: 10.1021/acs.inorgchem.6b02157 Inorg. Chem. XXXX, XXX, XXX−XXX
